No it isn't he is simply infertile it is that the Kanik Canik whatever bloodline is kind of like a different "species" is the best way to word it. She is "human" and he is "not". I am not sure how the bloodlines got mixed because of this race/species related infertility but it is said that at this point most everyone in Larkround is a mixed blood whereas FL is considered a pureblood human due to being part of the royal line. He is infertile but only because she has no Canik/Kanik blood from the way I understand it. He could have a baby with pretty much anyone but her.
So it's weird, and the story's explanation of this is weird but its supposedly because she is a pureblood, the royals don't mix with outsiders.
People from his clan/bloodline can't have children unless the other person shared their blood.
It doesn't make much sense in terms of blood since humans are the same species but it's a fictional world. What Emotional has said is quite brilliant, within this story bloodline is a bit like "species" are in our world.
Honestly, emotional brings up a brilliant question I have been wondering about as well. If purebloods and the others can't mix, how did the bloodlines mix up in the first place? That is indeed a mystery. My personal headcanon is that they could mix untill a certain point where some kind of a genetic mutation that has spread through most of their population occurred. I would assume this to be a super long process (hundreds or thousands of years depending on how big their population is, cuz the gene would need to be spread which would take a while.)
why tf she can't have a child? i don't fcking understand. PLEASE SOMEONE TELL ME WHY